Richard, I have been to London countless amounts of times. It was were I was born and lived for the first few months of my life. I still go back quite a few times every year. I have seen a lot of the sites so will try to pass you on as much as I can.
How long will you be going for? Hilton London Kensington Hotel, I presume is a excellent place to stay. I know kensington is a very good area of London and Hilton is worldwide reknowned prestigious hotel name.
Recommendations... Where do I start? Visit a few of the landmarks in the west end.
Covent Garden is a great place, you will always find a few streets performers there, the people that act like statues and really good food and shops around. I usually go back every time I visit.
Leicester Square is just down the road from Covent Garden, walking distance. I know you can hire these pedicabs just outside the tube station. lol! Leicester Square is known for all the premiers of new movies out. Dander around it and see how many people ask you if you would like to buy some theatre tickets.
Trafalgar Square is probably where you will met thousands of piegons.That would be good to visit mainly on a good day (unlikely).
Piccadlily Circus is another place, Might be worth a look at. You could take the tube to view these places yourself or you could purchase a London sightseeing pass at Baker Street, which is where they depart and return too.
Also up the road from that on Baker Street is where Madame Tussauds is. I loved that place and I hope you get to visit it. You do all sorts of things. Have a look on there website for more info but I'll tell you that you will enjoy yourself.
Another thing you may be interested in doing a tour of Jack the Ripper. I went on this, and I think it was very good. You walk a bit but I enjoyed it. Don't go with London Walks though. These people were very good and it is not usually a huge group -
http://www.jack-the-ripper-tours.com/
If you would like to meet some mad people then head down to camden. It has a few great markets which you may like to google. That might not be on top of your list because every second person is either a goth, emo or skater. Would be an interesting place to see but you may want to give it a pass.
There are alot of great museums is London, well of what I have heard. I haven't actually been to any but may be worth looking into. I think there is also one in Covent Garden but I may be wrong.
I'll finish off here, Take a look at the tours that go around the tower of London. You may just like to walk around or there are guided tours. It is really interesting in my opinion and well worth a visit.
The London eye is good although when I went I think you are queing for longer than you are actually up in it. It may be worth doing if you like.
I know you will not get all this done, but I hope there is a few suggestions that you may be interested in doing. By all means, please ask me anything you like or if there is anything I can do to help you in your visit to London, just let me know, here or email.